On generalized composite fractional q-derivative

  • Mridula Garg Department of Mathematics, University of Rajasthan, Jaipur - 302004, Rajasthan, India
  • Subhash Alha Department of Mathematics, University of Rajasthan, Jaipur - 302004, Rajasthan, India
  • Lata Chanchlani Department of Mathematics, S. S. Jain Subodh Girls College, Jaipur 302011, Rajasthan, India
Keywords: q-Laplace transform, q-integrals and q-derivatives

Abstract

In the present paper, we define a generalized composite fractional q-derivative D^{\alpha,\beta,\nu}_q and obtain some results for it. These results are image of power function under D^{\alpha,\beta,\nu}_q,  composition of Riemann-Liouville type fractional q-integral I^\alpha_q with D^{\alpha,\beta,\nu}_q  and q-Laplace transform of D^{\alpha,\beta,\nu}_q. We also obtain solution of a q-difference equation with derivative as D^{\alpha,\beta,\nu}_q  and discuss some special cases. A q-difference equation of D^{\alpha,\beta,\nu}_q  is solved using q-Laplace transform and its inverse.

Published
2015-11-10
Section
Articoli